Geometry Unit Study
Math topics are not often considered fodder for unit studies. Most people have a figure or number oriented view of mathematics. They think in terms of number sentences, problems and formulas. From that point of view it can be difficult to see all the possibilities for language, history and science study that can be found in a mathematical topic. Naturally visual, geometry works well as a first mathematical unit study.
Geometry is often offered piecemeal throughout most curriculums. In the early grades it is usually given a chapter in math texts. Saxon math books sprinkle it all the way through their upper elementary, junior high and high school level books. Eventually in high school, geometry is given an entire year in most curriculums. Key Curriculum Press is unique in offering a geometry curriculum for the upper elementary years called Key to Geometry, a part of the Key To series.
If you’re using a math text nothing says you can’t stop when you get to the geometry chapter and do an entire unit study on geometry. You can use your textbook to supply the typical approach to geometry while you add in all the extras that will make the subject come alive for your kids.
A good approach to starting any unit study is to ask your children what they already know about the subject. In this case, “What is geometry?” Have your children write the answer to that question or record their answers yourself. You can ask the question again at the end of the unit study to determine what they have learned. Throughout a unit study on math, it is a good idea to have your children write explanations of what they are learning. You can expect your children to have varying ability to turn mathematical thoughts into verbal expression. It is a skill that must develop, and for some develops quite slowly. Don’t be concerned that your child isn’t learning all you think he should have learned. He may not yet be able to verbalize his learning well.
Verbalizing mathematical concepts is one of the language arts activities you can do for your unit study. You can do further language arts work by writing mathematical stories. Write and illustrate a story where all the characters are geometric shapes. Possible story titles: I was a Teenage Triangle, The Circle That Wanted to Be a Square, The Case of the Missing Rectangle, or A Visit to Shapeville. Make a vocabulary list of geometry terms. Use them as your spelling words, too. Read some of the many picture books that have a geometry theme. Math oriented picture books are good reading even for upper elementary children.
The Librarian Who Measured the Earth tells how Erathosthenes used geometry to measure the earth in the 3rd century BC, before he or anyone else had ever traveled completely around the earth. Look for biographies of famous geometers such as Archimedes, Rene Descartes, Euclid, Carl F. Gauss, and Pythagoras to discover the history of geometry.
Look into various jobs and activities that require geometry. Engineering, surveying, navigation, mechanical drawing and architecture all use geometry. Books like Messing Around with Drinking Straw Construction which introduces kids to the principle of structural engineering provide fun hands on activities. The Creating Line Designs series is a great introduction to mechanical drawing. A Blueprint for Geometry turns your child into the architect and general contractor for a house he designs.
As with any unit study, a geometry unit can be as in depth or far ranging as you decide to make it. Each year you can focus on a different aspect of geometry. By the time your child is ready for high school geometry, they’ll be looking forward to it.
Compare basic geometric shapes to each other. For example, compare a square and a circle. What makes them the same? How are they different? Put a dot on the center point of each shape. Are the sides of the shape all the same distance from the middle point? What happens if you make a tile pattern from each of the shapes? The squares can go side by side, but the circles leave lots more background showing through.
Using a geoboard try to make a shape that has more sides than angles. Try to make a shape that has more angles than sides. Can it be done?
Use your geoboards to make the following shapes: polygon, triangle, square, rectangle, quadrilateral, pentagon, and hexagon. How would you show a line segment on a geoboard?
Use two 3 inch squares of paper of different colors to make two right angle triangles. See how many different shapes you can make using all four triangles. Make a sample sheet for each type of shape you make. You’ll need a sample sheet for triangles, quadrilaterals, pentagons, and hexagons. Draw each shape you make on its sample sheet. Make sure you don’t draw two of the same kind. Sometimes you need to rotate your shapes to make sure you don’t make duplicates. Use your triangles to make color patterns for one or more of the shapes you made. How many color patterns are possible for your shape?
Using the pieces of a tangram puzzle see how many different squares you can make from one or more pieces. Use the pieces to make triangles, rectangles, trapezoids, and parallelograms. Make a chart showing how you made each shape.
Experiment with tangram puzzle pieces to make your own shapes. When you’ve found a shape that you really like trace its outline on a piece of paper. Give it a name. Have someone else try to fill your shape with tangram puzzle pieces.
Glue toothpicks onto construction paper making geometric designs. Make a toothpick picture from geometric shapes. Flowers can be made from triangles, with lines for the stem and diamonds for the leaves. Break toothpicks into pieces to make an octagon for the sun. What else can you make using toothpicks?
Do some paper folding. Take a square of paper and see how many different shapes you can make by folding it different ways. Get an origami book and origami paper and make paper folding creations.
Make paper snowflakes and discuss symmetry. How do you fold your paper to make an asymmetrical snowflake? What happens when you cut an asymmetrical snowflake? How do you fold your paper to get a six-sided or an eight-sided snowflake? Cut out pictures from magazines. Fold them to see if they are symmetrical. Make a poster with symmetrical pictures on one side and asymmetrical pictures on the other side.
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